In this paper, a two-dimensional model for the growth of multi-layer tumors
is presented. The model consists of a free boundary problem for the tumor cell
membrane and the tumor is supposed to grow or shrink due to cell proliferation
or cell dead. The growth process is caused by a diffusing nutrient
concentration Ο and is controlled by an internal cell pressure p. We
assume that the tumor occupies a strip-like domain with a fixed boundary at
y=0 and a free boundary y=Ο(x), where Ο is a 2Ο-periodic
function. First, we prove the existence of solutions (Ο,p,Ο) and that
the model allows for peculiar stationary solutions. As a main result we
establish that these equilibrium points are locally asymptotically stable under
small perturbations.Comment: 15 pages, 2 figure